It could be a lot of things in otherwise normal cats (cats who don't have feline leukemia, or other immunosuppressive disease).
1. Not enough antibiotic. Are you sure that your cat received all of the antibiotic? Some cats are very good at hiding pills.
2. Not taking the antibiotic for a long enough period of time.
3. Inappropriate antibiotic.
4. Combination infection: more than one bacterial agent in the urine, or uroliths (stones in the bladder), or crystals.
5. Urinary tract infection with interstitial nephritis.
7. Tumor in the bladder.
8. Kidney or vaginal infection.
9. Unknown causes
10. A combination of two or more of the above.
When a cat gets a urinary tract infection the cat is usually placed on a first line antibiotic for approximately two weeks. At the end of the two week period another urine sample must be analysed to see if the infection is gone. If the urine still contains infection the antibiotics are continued for another period of time and the urinalysis is repeated at the end of the second course of antibiotics.
If after this last urinalysis the urine still contains bacteria, white blood cells or blood, than it is appropriate to have abdominal X-Rays performed to see if there are any stones in the bladder or kidneys. A urine culture and sensitivity should also be performed, but the cat must be off of antibiotics for at least a few days for an accurate culture and sensitivity result. The culture and sensitivity will determine exactly what bacteria is causing the infection and what the correct antibiotic should be.
Occasionally the culture and sensitivity comes back negative; this occurs either due to the cat not being off the antibiotic for a long enough period of time for an accurate result, or due to interstitial nephritis, or other non-infectious cause.
So please call your vet and at least discuss your cat's relapse.